Laser. emission W FL

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1 W Laser Laser emission W FL Supplementary Figure 1. Comparison between fluorescence and laser emission spectra. The fluorescence has broad spectrum whereas the laser has very narrow spectrum. W FL and W Laser are the spectral width for fluorescence and laser emission, respectively. is the laser wavelength. FL 1

2 a [E]=4 1 b Laser output Fluorescence c Time (s) [E]=2 [E]=1 [E]=.5 [E]=4 [E]=2 [E]=1 [E]=.5 Fluorescence Laser output d Time (s) Time (s) Time (s) Supplementary Figure 2. Comparison between fluorescence and laser emission from the same enzyme-substrate reaction. (a,b) Fluorescence based on Supplementary Equation 3 plotted in the linear-linear and log-log scale. The intensity of the fluorescence at a fixed time (illustrated by the vertical dashed line in (a)) is used in the traditional ELSA to quantify the analyte. (c,d) Laser emission based on Supplementary Equation 16 plotted in the linear-linear and log-log scale. The laser onset time, which is marked by arrows, is used in the optofluidic laser based ELSA to quantify the analytes. The enzyme concentration varies from.5 to 4. A =.5, k =.1 s -1, = 2, W FL = 1, B =.4, [S] = 1, W Laser =.1 and =.1. 2

3 Supplementary Figure 3. (a,b) Cross-sectional and top view of the FP optofluidic laser cavity. The fluidic channel, which had a 1 mm x 1 mm cross section and a wall thickness of 15 m, was sandwiched between two gold mirrors. The top mirror was 1 mm wide so that the light could excite the laser from the left or right side of the gold stripe (see Supplementary Figure 4). (c) Picture of optofluidic laser arrays. 3

4 Supplementary Figure 4. Experimental setup. The optofluidic laser was excited by a pulsed optical parametric oscillator (OPO) at 532 nm from one side of the fluidic channel. Both fluorescence and laser emission were collected through the top mirror and sent to a spectrometer. 4

5 1 1 t 2-1 (min -1 ) (min -1 ) HRP concentration (ng ml -1 ).1 Supplementary Figure 5. nverse of the laser onset time () and inverse of the time for the fluorescence peak to reach 2 counts (t 2 ), both extracted from Fig. 4, as a function of the HRP concentration. The slope of both linear fits in the log-log scale is about 1.2, close to 1 predicted by Eqs. (1) and (4) in the main text. The laser onset time is defined as the time when laser intensity reaches 1 (counts from CCD) in Fig. 4. Error bars are obtained based on triplicate measurements. 5

6 6 Emission (a.u.) 4 2 Black: [L-6]=1 fg ml -1, =422 min Red: [L-6]=1 fg ml -1, =36 min Wavelength (nm) Supplementary Figure 6. Emission spectra near the laser onset time for two different analyte concentrations. Laser emission is superimposed on fluorescence emission. Black curve: L-6 concentration = 1 fg ml -1, laser onset time = 422 min; Red curve: L-6 concentration = 1 fg ml -1, laser onset time = 36 min. 6

7 3 Black: [L-6]=1 fg ml -1 Red: [L-6]=1 fg ml -1 6 min 4 Fluorescence (a.u.) min 18 min 24 min 3 min Fluorescen peak fg ml -1 1 fg ml Wavelength (nm) Time (min) Supplementary Figure 7. (a) ndistinguishable fluorescence spectra taken at different enzyme-substrate reaction times for L-6 concentration of 1 fg ml -1 (black curves) and 1 fg ml -1 (red curves), respectively. (b) Fluorescence peak around 587 nm extracted from (a). 7

8 1 6 a 3x1 3 b Laser intensity (a.u.) Fluorescence (a.u.) 2x1 3 1x1 3 3 min 6 min Time (min) Wavelength (nm) Supplementary Figure 8. (a) The onset time for laser resulting from nonspecific bindings (when [L-6] = fg ml -1 ) was ns = 455 min (when laser intensity = 1). (b) The peak of fluorescence resulting (around 587 nm) from non-specific bindings after 6 minutes and 3 minutes of enzymesubstrate reaction was FL ns = 92 counts and FL ns = 2265 counts, respectively. 8

9 Sword Diagnostics R&D System QuantiGlo R&D System Quantikine R&D System Quantikine HS nvitrogen ELSA Kit nvitrogen ELSA Kit Ultrasensitive Optofluidic laser ELSA L-6 concentration (pg ml -1 ) Supplementary Figure 9. Comparison of various ELSA L-6 assays 1. 9

10 1 6 FL-FL ns min extrapolated 48 min min [L-6] (fg ml -1 ) Supplementary Figure 1. The fluorescence peak around 587 obtained at 2 minutes and 48 minutes of reaction time. The open triangles are obtained by linearly extrapolating the fluorescence to 48 minutes. The solid and dash lines are the linear fit in the log-log scale for the L-6 concentrations above 1 fg ml -1. Error bars are obtained based on triplicate measurements. The experimental details are described in Methods in the main text. 1

11 Supplementary Figure 11. (a) Experimental setup for the optofluidic ring resonator (OFRR) laser based ELSA. The optofluidic ring resonator was made of a fused silica capillary (inner diameter = 76 m). The optical feedback is provided by the whispering gallery mode that circulates along the OFRR circumference. The enzyme-substrate reaction for ELSA occurred on the inner surface of the capillary and the resultant fluorescent products filled the entire capillary. (b) Optofluidic laser emission spectra for various enzyme-substrate reaction times. Curves are vertically shifted for clarity. L-6 concentration = 1 pg ml -1. The energy density was fixed at J mm -2 per pulse. 11

12 Laser intensity (a.u.) pg ml -1 1 pg ml -1 1 pg ml -1 pg ml Time (min) Supplementary Figure 12. Optofluidic ring resonator laser based ELSA measurement for various concentrations of L-6 plotted in the linear-log scale. Spectral integration for laser output takes place from 59 nm to 635 nm in Supplementary Figure 11b. The laser onset time was 377 min, 39 min, min and 61.5 min, respectively, for [L-6] = pg ml -1, 1 pg ml -1, 1 pg ml -1 and 1 pg ml -1. The energy density was fixed at J mm -2 per pulse. 12

13 Supplementary Note 1: Theoretical Analysis Note: n our calculation, all intensities are normalized to the saturation intensity defined as Sat = h/(), where h is the Planck constant and is emission frequency. and are the fluorophore absorption cross section and lifetime, respectively. Therefore, the intensity here is dimensionless. Traditional ELSA measurement The enzyme-substrate reaction generates the fluorescent product over time. According to the Michaelis-Menten equation, the concentration of the product, [P], can be written as: [ P] k [ E] t, (1) where [E] is the concentration of the enzyme within a given volume, and in ELSA, is linearly proportional to the number of the analytes captured on the solid surface. k and t are the rate constant and the enzyme-substrate reaction time, respectively. The total fluorescence intensity is given by: FL A [ P] A k [ E] t, (2) where is the external excitation and A is a constant that takes into account the absorption coefficient and quantum yield of the product, as well as other factors such as the detection volume and the light collection efficiency. The traditional ELSA detection measures the fluorescence signal at a fixed reaction time, t. For simplicity, we assume the fluorescence spectrum is flat with a bandwidth of W FL (see Supplementary Figure 1). Therefore, the fluorescence peak height at is: FL ( ) FL / WFL A k [ E] t / WFL. (3) FL and hence ( ) quantify the number of the enzymes in the detection volume, which, in ELSA detection, corresponds to the number of the captured analytes on the solid surface. The fluorescence based on Supplementary Equation 3 is plotted in Supplementary Figure 2a and b. t can be seen easily from Supplementary Figure 2a that, with the deceased enzyme (and hence analyte) concentration, the difference of the two fluorescence signals caused by the two different enzyme concentrations decreases, i.e., FL( ) A k [ E] t / WFL. (4) Eventually, the fluorescence height variation is below the noise level at,, at which point the two enzyme concentrations become indiscernible. Therefore, [ E] min. (5) A k t / W FL Alternatively, we can also use the time, t, for the enzyme-substrate reaction to reach a certain level of fluorescence, ( ), as the sensing signal. Based on Supplementary Equation 3, the sensing signal can be expressed as: FL( ) t. (6) A k [ E]/ WFL A small change in [E] will lead to a change in t and therefore we have: 13

14 FL( ) t [ E] min. 2 (7) A k [ E] / WFL where t is the noise in time measurement. Since the uncertainty in time measurement is determined by the uncertainty in the intensity measurement (ignoring all other types of noises), i.e., t. (8) A k [ E]/ WFL we arrive at: [ E] min, (9) A k t / WFL which is the same as Supplementary Equation 5. This result suggests that in comparison with fluorescence intensity measurement the time measurement does not improve the sensing performance in the traditional ELSA. Optofluidic laser based ELSA Laser emission is illustrated in Supplementary Figure 1. Based on our earlier theoretical work about an optofluidic laser in general 2-4, the lasing threshold condition is expressed as: n1 e ( ) ([ S] n1 ) a ( ) Lc, (1) where [S] is the total concentration of the substrate and the product, which is equal to the initial concentration of the substrate. n 1 is the concentration of the product in the excited state. e is the product emission cross section at the lasing wavelength ( ). a is the substrate and product absorption cross section at the lasing wavelength ( ). Without losing generality, we assume that both substrate and product have the same absorption cross section at. L c is the cavity loss coefficient. At the threshold, Supplementary Equation 1 becomes: n1 a Lc (1 ). (11) [ S] e a [ S] a Note that depends on the characteristics of the optical cavity, the emission/absorption cross section of the substrate, and the initial concentration of the substrate, all of which are fixed in the optofluidic ELSA measurement for a given laser based ELSA system. Using the rate equations for a four-energy-level system, n 1 given by 5 : n 1, (12) [ P] 1 which calculates the fraction of the products that are ed to the excited state under a given external,. Rewriting Supplementary Equation 12, we arrive at an important lasing threshold condition:, th [ P]/[ S] f (13) where f=[p]/[s] is the fraction of the substrates converted into the fluorescent products. Note that Supplementary Equation 13 is valid only when f>=, as is a subset of f that is in the excited state at the lasing threshold. 14

15 According to the laser theory, the laser output power is linearly proportional to the intensity,, above the lasing threshold 5 : Laser B ( 1), (14) th where B is a constant. Considering Supplementary Equation 13, we arrive at f B [ ( 1) 1]. The laser peak height is given by: B f ( ) [ ( 1) 1], WLaser where W Laser is the linewidth of the laser emission. Laser (15) Laser (16) n the laser based ELSA, and are fixed for a given laser system with a given substrate. [P] increases over time according to Supplementary Equation 1. nitially, f [ P]/[ S ], which is non-physical and the laser would never be achievable. When f, the laser can potentially be achieved, depending on. With further increase in [P] over time, th continues to decrease and eventually reaches the point where th =. The laser onset time,, is defined as the time when [P] reaches the threshold concentration, [P] threshold, such that th = and the laser starts to emerge. Beyond the onset time, the laser output follows Supplementary Equation 15. The laser output based on Supplementary Equation 16 is plotted in Supplementary Figure 2c and d, exhibiting the well-known threshold characteristics. Note that although above the lasing onset time the laser output is linearly dependent upon time, the discontinuity caused by the threshold in the laser curve results in fundamental difference between the laser output near the onset time and fluorescence. Near the onset time the laser output increases drastically in the log-log scale (Supplementary Figure 2d). n contrast, the slope is unity for fluorescence all the time (Supplementary Figure 2b). The optofluidic laser based ELSA employs the laser onset time,, as the sensing signal. For a given optofluidic laser system where and are fixed, [P] threshold is constant. Therefore, the laser onset time,, can be expressed as: [ P] threshold /([ E] k) C /[ E], (17) where C is a constant. Through Supplementary Equation 17, the detection of enzyme concentration [E] becomes determining the laser onset time. t should be emphasized that the sensing signal, in Supplementary Equation 17, is inversely proportional to the enzyme concentration [E]. Therefore, the optofluidic laser method is particularly useful to detect low concentrations of analytes, for which a small [E] and hence a large are anticipated. Based on Supplementary Equation 17 we have 2 CE /[ E]. (18) t can be seen easily that with the decreased analyte (and hence enzyme) concentration, the difference of the two onset times caused by the two different enzyme concentrations increases. This is opposite to the traditional ELSA described previously. t should also be noted that the laser onset time depends on the fluorescent product concentration, but not on the total number of the fluorescent products. This is advantageous over intensity based detection in the traditional 15

16 ELSA when microfluidic systems are used, where the total number of fluorescent molecules decreases significantly in comparison with conventional fluidic systems (such as 96-well plates). Comparison between fluorescence and laser based detection We compare the fluorescence based detection with the laser based detection to find out which method provides more accurate time measurement. n order to identify a laser peak, the laser peak at, ( ) should rise above the noise,. Based on Supplementary Equation 16, we have: [ P] Laser( ) B. (19) WLaser [ S] However, detailed calculation of the relation between ( ) and P] is difficult through Supplementary Equation 19 due to the lack of the detailed information of the substrate and the product. Alternatively, we can rely on energy conservation to compare directly the laser system and the fluorescence system. For a laser, nearly all the energy absorbed by the fluorescent product is converted to the lasing emission (except a negligible fluorescence background). Therefore, we have: Laser ( ) D [ P]/ W Laser D k [ E] t / W Laser, (2) where D is a constant that takes into account the absorption coefficient and quantum yield of the product, as well as other factors such as the detection volume and the light collection efficiency. Therefore, the uncertainty in time determination is given by: t. (21) D k [ E]/ WLaser Comparing with the fluorescence method (Supplementary Equation 8), we find that D is usually larger than A due to larger light collection efficiency (directional laser emission) and higher quantum yield. Furthermore, because of much narrower emission band, W Laser << W FL. As a result, the laser provides much higher accuracy in time measurement. For example, everything else being equal, 1- to 1-fold improvement can be obtained by simply considering the narrow laser linewidth (<< 1 nm) in comparison with the broad linewidth in fluorescence (~5 nm). n practice, it is easier to determine the laser onset time by relying on the extremely sharp slope of the laser output vs. time in the log-log scale, which arises from the threshold nature of the laser. n the log-log scale, we have: t 1, (22) ( ) K where K is the slope in the log-log scale, and, for the laser emission, it is on the order of 1 2 whereas it is unity for fluorescence (see Fig. 2b and d, and Fig. 4b). Therefore, the laser onset time can be determined accurately. n the experiment presented in the Article, we define the laser onset time as the laser emission reaches 1 counts on the CCD in the spectrometer. 16

17 Supplementary Note 2: Estimation of HRP Surface Density The laser cavity had an inner dimension of approximately 1 mm x 1 mm x 1 mm (i.e., detection volume = 1 L and inner surface area of 4 mm 2 ). Based on Fig. 4b in the main text,.5 ng ml -1 of HRP (or 6.8x1 6 HRP molecules in the detection volume, assuming that the HRP molecular weight is 44 kd) reacted with the substrate and the product reached the threshold concentration in 62 minutes. Within the same detection volume, it took the non-specifically bound HRP 455 minutes to reach the same product threshold concentration. Based on Supplementary Equation 17 and considering the small difference in the excitation (1244 J mm -2 vs. 187 J mm -2 ), it is estimated that only 6.2x1 5 HRP molecules were attached to the laser cavity inner surface, which corresponded to a HRP surface density of 1.6x1 7 cm -2. Such a level of non-specific binding is deemed as high, as compared to that in digital ELSA 6, which requires the average number of enzymes on a 2.7-m diameter microbead be far below 1% (corresponding to a surface density of 4.4x1 5 cm -2 ). 17

18 Supplementary Note 3: Optofluidic Laser Based ELSA with a Ring Resonator To demonstrate the broad applicability of the optofluidic laser based ELSA principle, we also carried out similar experiments using an optofluidic ring resonator (OFRR) as the laser cavity. The OFRR is based on a thin-walled glass capillary whose circular cross section forms a ring resonator that supports the whispering gallery mode (WGM). The WGM has an evanescent field inside the capillary and thus provides optical feedback needed for lasing. Details of the OFRR laser can be found in our previous work 2,3,7-1. The experimental setup is shown in Supplementary Figure 11a and examples of the lasing spectra for one ELSA measurement are presented in Supplementary Figure 11b. The laser ouptput intensity as a function of enzymesubstrate reaction time is given in Supplementary Figure 12, showing distinct threshold characteristics and clear difference in the laser onset time for different analyte concentrations. 18

19 Supplementary References 1 Sword Diagnostics nc, High sensitivity Human L-6 ELSA with an expanded dynamic range: enhanced performance using Sword TM peroxidase assay and the Tecan nfinite M1 multimode reader. (214). 2 Sun, Y. & Fan, X. Distinguishing DNA by analog-to-digital-like conversion by using optofluidic lasers. Angew. Chem. nt. Ed. 51, (212). 3 Lee, W. & Fan, X. ntracavity DNA melting analysis with optofluidic lasers. Anal. Chem. 84, (212). 4 Fan, X. & Yun, S.-H. The potential of optofluidic biolasers. Nat. Methods 11, (214). 5 Siegman, A. E. Lasers. (University Science Books, 1986). 6 Rissin, D. M. et al. Single-molecule enzyme-linked immunosorbent assay detects serum proteins at subfemtomolar concentrations. Nat. Biotechnol. 28, (21). 7 Sun, Y., Shopova, S.., Wu, C.-S., Arnold, S. & Fan, X. Bioinspired optofluidic FRET lasers via DNA scaffolds. Proc. Natl. Acad. Sci. USA 17, (21). 8 Zhang, X., Lee, W. & Fan, X. Bio-switchable optofluidic lasers based on DNA Holliday junctions. Lab Chip 12, (212). 9 Chen, Q. et al. Highly sensitive fluorescent protein FRET detection using optofluidic lasers. Lab Chip 13, (213). 1 Wu, X., Chen, Q., Sun, Y. & Fan, X. Bio-inspired optofluidic lasers with luciferin. Appl. Phys. Lett. 12, 2376 (213). 19